Where are the zeros and what is the value of x between [-1,1]?

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Homework Help Overview

The discussion revolves around finding the zeros of the polynomial function 5x^3 - 2x^2 + 3 within the interval [-1, 1]. Participants are exploring the existence of roots in this range.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss evaluating the polynomial at the endpoints of the interval to determine the signs of the function, which may indicate the presence of a root. There is also mention of graphing the function to visually assess where it crosses the x-axis.

Discussion Status

Some participants have provided numerical estimates for potential zeros, while others have suggested methods for checking the function's behavior at specific points. There is no explicit consensus on the exact location of the zeros, and multiple interpretations of the problem are being explored.

Contextual Notes

There are indications of potential errors in previous responses regarding the location of the zeros, and participants are encouraged to verify their findings through evaluation and graphing.

assman
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5x^3 - 2x^2 + 3

Where are the zeros. Is there one between [-1,1]

THanks.
 
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There is a zero at (-0.7860031,0)
 
Evaluate the expression at x = -1 and x = 1.

What are the signs of the expression at these two points? What does this tell you about whether or not there is at least one root between them (hint: plot the two points and draw a line through them. Does it cross 0?) ?

--J
 
UrbanXrisis, that is the wrong answer.
 
ACK! Sorry! (-0.7290014,0) Typed in the wrong answer
 
The easiest way to solve that for you might be to graph the equation. Then limit you window from in the x from -2 to 2 then see if it crosses the axis between -1 and 1... zoom out to see all the zeros if more exist.
 
I think x would -0.92 if it is like this
5x^3 - 2x^2 + 3=0
 

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